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Simplifying 0 = x2 + 24x + -128 Reorder the terms: 0 = -128 + 24x + x2 Solving 0 = -128 + 24x + x2 Solving for variable 'x'. Combine like terms: 0 + 128 = 128 128 + -24x + -1x2 = -128 + 24x + x2 + 128 + -24x + -1x2 Reorder the terms: 128 + -24x + -1x2 = -128 + 128 + 24x + -24x + x2 + -1x2 Combine like terms: -128 + 128 = 0 128 + -24x + -1x2 = 0 + 24x + -24x + x2 + -1x2 128 + -24x + -1x2 = 24x + -24x + x2 + -1x2 Combine like terms: 24x + -24x = 0 128 + -24x + -1x2 = 0 + x2 + -1x2 128 + -24x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 128 + -24x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -128 + 24x + x2 = 0 Move the constant term to the right: Add '128' to each side of the equation. -128 + 24x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + 24x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 24x + x2 = 0 + 128 24x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 24x + x2 = 128 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 128 + 144 Reorder the terms: 144 + 24x + x2 = 128 + 144 Combine like terms: 128 + 144 = 272 144 + 24x + x2 = 272 Factor a perfect square on the left side: (x + 12)(x + 12) = 272 Calculate the square root of the right side: 16.492422502 Break this problem into two subproblems by setting (x + 12) equal to 16.492422502 and -16.492422502.Subproblem 1
x + 12 = 16.492422502 Simplifying x + 12 = 16.492422502 Reorder the terms: 12 + x = 16.492422502 Solving 12 + x = 16.492422502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 16.492422502 + -12 Combine like terms: 12 + -12 = 0 0 + x = 16.492422502 + -12 x = 16.492422502 + -12 Combine like terms: 16.492422502 + -12 = 4.492422502 x = 4.492422502 Simplifying x = 4.492422502Subproblem 2
x + 12 = -16.492422502 Simplifying x + 12 = -16.492422502 Reorder the terms: 12 + x = -16.492422502 Solving 12 + x = -16.492422502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -16.492422502 + -12 Combine like terms: 12 + -12 = 0 0 + x = -16.492422502 + -12 x = -16.492422502 + -12 Combine like terms: -16.492422502 + -12 = -28.492422502 x = -28.492422502 Simplifying x = -28.492422502Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.492422502, -28.492422502}
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